The effect of finite turbulence spatial scale on the amplification of turbulence by a contracting stream

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Abstract
An alternative to Hunt's (1973) extension of classical rapid distortion theory is used to calculate the turbulence downstream of a rapid contraction. This problem was originally studied by Batchelor & Proudman (1954) and Ribner & Tucker (1953), but their analyses were restricted to flows in which the characteristic turbulence scales were small compared to the spatial scales of the mean flow (usually the characteristic dimension of the apparatus). We now consider the case where the turbulence scale can have the same magnitude as the mean-flow spatial scale. Relatively simple formulae are obtained by calculating the turbulence only in the downstream region where the mean flow is no longer affected by the potential field of the contraction.The results are then further simplified by assuming that the contraction is large and expanding in inverse powers of the contraction ratio. The calculations show that effects of finite turbulence scale can be quite significant. We also obtain some important new results for small-scale turbulence by expanding the solutions in inverse powers of the turbulence spatial scale.

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